The greatsword is already pretty much the most powerful martial weapon in the game, so we have to be careful before adding in abilities to make it even more powerful. A prestige class to make it more versatile, I think that can work.
2x Str mod in particular is very powerful, due to how high your Strength score can get at high levels. It's too powerful to give out unless you limit how often it can be used. Once per day per two levels in a prestige class, I think that's fair.
In the APG the two handed fighter archetype allows for double strength when wielding two handed weapons when making a full attack, so maybe a similar ability or just the same carried over?